Numerical design and CFD validation of a low Reynolds number orifice flow meter

This work aims at designing an affordable digital flow meter suitable for air flows encountered in biotechnology laboratories (10 to 1 000 Nml/min, in 4 to 8 mm diameter pipes, under 1 to 8 bar). It builds on the classical orifice flow meter designs (pressure difference-based and robust) and recent pressure sensors improvement (allowing one sensor to measure from 1 to 10 000 Pa). While orifice flow meters are well-established for turbulent regimes, owing to their ability to deliver an almost constant discharge coefficient value, their application in low Reynolds number conditions (such as the ones above) is underrepresented. In these conditions, the pressure difference strongly depends on the Reynolds number, potentially posing a challenge. To address it, this article aims to derive design guidance for low Reynolds number cases, using a numerical workflow, based on the CFD framework OpenFOAM. Taking advantage of recent turbulence development of transitional turbulence, it is able to cover laminar, transition, and turbulent regimes. The predictions were extensively validated against experimental data (average MAPE of 5.43 %, NSE of 0.98, and CCC of 0.99). Once confidence has been built, the numerical workflow was used to explore the targeted design-space ( β ratio from 0.0375 to 0.10, t ∗ ratio from 1.0 to 2.0, and Reynolds number from 1 to 400). Results aligned with established design principles: a low β ratio and high dimensionless thickness ( t ∗ ) are needed to ensure a measurable pressure difference. Two candidate designs emerge: β = 0.11 and t ∗ = 1.75, and β = 0.0625 and t ∗ = 1/8. Still, from a practical point of view, a machining tolerance analysis showed that realizing the optimal system could be quite a feat. Specifically, it requires drilling a very small orifice diameter (0.25 or 0.44 mm) while demanding tight machining tolerances ( ± 0.01 mm), making fabrication non-trivial. Overall, the study demonstrates that a low Reynolds number orifice flow meter for biotechnology applications is technically feasible, but its practical implementation requires precise manufacturing or external calibration of each of the units.